This invention relates to the art of oscillators, and more particularly, to predicting the phase noise of oscillators for use in designing and building oscillators that meet prescribed conditions.
Oscillators are used in many circuits. In particular, with regard to oscillators for use in wireless, e.g., radio, communications, the accuracy of the frequency of the oscillator employed is very important in determining the channel selectivity, i.e., the ability to discriminate between different adjacent channels. Phase noise, also known as timing jitter, is the main factor that determines the frequency accuracy. Thus, it is necessary that the oscillator employed have no more than a prescribed amount of phase noise.
It is known that it is desirable to simulate an oscillator to determine its phase noise prior to actually building the oscillator, in order to be sure that the oscillator does not exceed the prescribed amount of phase noise. However, prior art techniques for determining the phase noise of an oscillator either are very slow or are inaccurate predictors of the actual phase noise experienced when the oscillator is actually built.
We have recognized that the phase noise of an oscillator described by a known set of differential algebraic equations (DAEs) can be quickly and accurately predicted, in accordance with the principles of the invention, by a) finding the steady state waveform of the oscillator, e.g., by using harmonic balance techniques or so-called xe2x80x9cshootingxe2x80x9d techniques, either of which involves developing a mathematical quantity known as the augmented Jacobian matrix; b) solving a prescribed linear system of equations that uses the augmented Jacobian matrix, the solution being called a perturbation projection vector (PPV), c) plotting a graph of the phase noise of the oscillator as a Lorentzian function of the solution of the prescribed linear system of equations.
More specifically, in accordance with an aspect of the invention, the prescribed linear system of equations which is used is the system of equations formed by setting a matrix product equal to a unit vector. The factors in the matrix product are 1) a form of the augmented Jacobian matrix, e.g., the Hermitian, for use with the harmonic balance technique, or the adjoint, for use with shooting, and 2) the PPV. The variables of the
Lorentzian function of the solution of the prescribed linear system of equations includes 1) the frequency at which the phase noise is to be found, 2) a jitter factor determined for the oscillator, and 3) the steady state waveform of the oscillator, which includes the natural frequency of the oscillator. The jitter factor for the oscillator is determined in accordance with the method disclosed in our co-pending and commonly assigned U.S. patent application Ser. No. 09/096856, now issued as U.S. Pat. No. 6,167,359, which is incorporated by reference as if fully set forth herein, but using therein the PPV as described hereinabove. Note that a) that which is referred to herein as the PPV is referred to in U.S. patent application Ser. No.09/096856 as v,(t), and that which referred to herein as the jitter factor is referred to in U.S. patent application Ser. No. 09/096856 as c, all the other variables being as described in U.S. patent application Ser. No. 09/096856.